After several meetings, Athens and Skopje agreed on Tuesday that the country will be renamed the "Republic of North Macedonia" and that Macedonia should amend its constitution accordingly.
Critics of the deal, who organized opposition rallies in both countries in the days leading up to the announced agreement, repeated their objections on June 12 and signaled they will oppose its ratification.
The two prime ministers are expected to sign the agreement over the next weekend.
The dispute over the "Macedonia" name had been a thorn in relations of the two countries at least since 1991, when Macedonia broke away from former Yugoslavia, declaring its independence under the name Republic of Macedonia.
"We have a historic, centennial decision", Zaev said in a live web stream.
The Greek government will inform the European Union and NATO by letter that it supports the beginning of European Union accession talks and NATO accession for the Republic of North Macedonia, despite the reluctance by France and the Netherlands.More news: Raccoon scales Minnesota office tower, captivating public
But EU membership remains a decades-long prospect, while North Atlantic Treaty Organisation, as highlighted by Zaev's comment on "we're becoming a member", offers a more immediate security guarantee.
"Mr. Tsipras does not process the political legitimacy to bind Greece by signing an agreement that does not have the full support of his own government".
The name issue has been blocking Skopje's aspirations to join North Atlantic Treaty Organisation and the European Union for years. "The question is when will this happen because there are still hard times ahead".
Still, the leaders may face uphill battles in approving the deal.
Officials in Albania are hailing the agreement between bordering Greece and Macedonia to end their decades-long name dispute as good for the whole Western Balkans region.
Greece had objected to the name "Macedonia", fearing territorial claims on its eponymous northern region, as well as cultural appropriation of the Greek nature of Ancient Macedonia, a historically Greek province and important part of Ancient Greek history that has no direct connection between the modern citizens, who hail from a mixed Slavic heritage.More news: Dennis Rodman broke down in tears talking about North Korea-US situation
The announcement came after telephone talks with Greek counterpart, Alexis Tsipras, on Tuesday.
Zaev said his country will hold a national referendum in fall on the agreement. He has to muster a two-thirds parliamentary majority to change the country's constitution.
He is close to the nationalist VMRO-DPMNE party which was defeated by Zaev in elections a year ago. He has accused his predecessor, nationalist leader Nikola Gruevski, of deliberately fueling the rift with Greece.
"This historic agreement is testament to many years of patient diplomacy, and to the willingness of these two leaders to solve a dispute which has affected the region for too long", said NATO Secretary General Jens Stoltenberg in a statement. Tusk said: "Thanks to you the impossible is becoming possible", he said.
The "historic agreement" contributes "to the transformation of the entire region of south-east Europe", the European Union enlargement commissioner and foreign affairs chief, Johannes Hahn and Federica Mogherini, said.More news: Former UNI player Nick Nurse becoming Toronto Raptors' head coach
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